Related papers: Adaptive Topological Feature via Persistent Homolo…

We propose a neural network for 3D point cloud processing that exploits `spherical' convolution kernels and octree partitioning of space. The proposed metric-based spherical kernels systematically quantize point neighborhoods to identify…

Persistent homology is a technique recently developed in algebraic and computational topology well-suited to analysing structure in complex, high-dimensional data. In this paper, we exposit the theory of persistent homology from first…

This paper presents a mathematically rigorous framework for brain-inspired representation learning founded on the interplay between persistent topological structures and cohomological flows. Neural computation is reformulated as the…

Recent years have witnessed the great success of deep learning on various point cloud analysis tasks, e.g., classification and semantic segmentation. Since point cloud data is sparse and irregularly distributed, one key issue for point…

Recent progresses in 3D deep learning has shown that it is possible to design special convolution operators to consume point cloud data. However, a typical drawback is that rotation invariance is often not guaranteed, resulting in networks…

We propose a local-to-global representation learning algorithm for 3D point cloud data, which is appropriate to handle various geometric transformations, especially rotation, without explicit data augmentation with respect to the…

Persistent homology is a method for computing the topological features present in a given data. Recently, there has been much interest in the integration of persistent homology as a computational step in neural networks or deep learning. In…

In this work, we develop a pipeline that associates Persistence Diagrams to digital data via the most appropriate filtration for the type of data considered. Using a grid search approach, this pipeline determines optimal representation…

Topological data analysis is a relatively new branch of machine learning that excels in studying high dimensional data, and is theoretically known to be robust against noise. Meanwhile, data objects with mixed numeric and categorical…

Scene recognition, particularly for aerial and underwater images, often suffers from various types of degradation, such as blurring or overexposure. Previous works that focus on convolutional neural networks have been shown to be able to…

This paper proposes a novel topological learning framework that integrates networks of different sizes and topology through persistent homology. Such challenging task is made possible through the introduction of a computationally efficient…

In recent years, deep learning-based point cloud normal estimation has made great progress. However, existing methods mainly rely on the PCPNet dataset, leading to overfitting. In addition, the correlation between point clouds with…

This paper aims at bringing some light and understanding to the field of deep learning for dynamic point cloud processing. Specifically, we focus on the hierarchical features learning aspect, with the ultimate goal of understanding which…

Deep learning with 3D data such as reconstructed point clouds and CAD models has received great research interests recently. However, the capability of using point clouds with convolutional neural network has been so far not fully explored.…

Point clouds are an increasingly relevant data type but they are often corrupted by noise. We propose a deep neural network based on graph-convolutional layers that can elegantly deal with the permutation-invariance problem encountered by…

This paper presents Point Convolutional Neural Networks (PCNN): a novel framework for applying convolutional neural networks to point clouds. The framework consists of two operators: extension and restriction, mapping point cloud functions…

Estimation of differential geometric quantities in discrete 3D data representations is one of the crucial steps in the geometry processing pipeline. Specifically, estimating normals and sharp feature lines from raw point cloud helps improve…

This paper proposes a novel point-cloud-based place recognition system that adopts a deep learning approach for feature extraction. By using a convolutional neural network pre-trained on color images to extract features from a range image…

Point clouds are a popular representation for 3D shapes. However, they encode a particular sampling without accounting for shape priors or non-local information. We advocate for the use of a hierarchical Gaussian mixture model (hGMM), which…

Techniques from computational topology, in particular persistent homology, are becoming increasingly relevant for data analysis. Their stable metrics permit the use of many distance-based data analysis methods, such as multidimensional…